How is the basic structure of diamond related to its bulk properties?
1 answer:
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(a) 1440.5 Hz
The general formula for the Doppler effect is
where
f is the original frequency
f is the apparent frequency
is the velocity of the wave
is the velocity of the receiver (positive if the receiver is moving towards the source, negative otherwise)
is the velocity of the source (positive if the source is moving away from the receiver, negative otherwise)
Here we have
f = 1110 Hz
v = 334 m/s
In the reflector frame (= on surface B), we have also
(surface A is the source, which is moving towards the receiver)
(surface B is the receiver, which is moving towards the source)
So, the frequency observed in the reflector frame is
(b) 0.232 m
The wavelength of a wave is given by
where
v is the speed of the wave
f is the frequency
In the reflector frame,
f = 1440.5 Hz
So the wavelength is
(c) 1481.2 Hz
Again, we can use the same formula
In the source frame (= on surface A), we have
(surface B is now the source, since it reflects the wave, and it is moving towards the receiver)
(surface A is now the receiver, which is moving towards the source)
So, the frequency observed in the source frame is
(d) 0.225 m
The wavelength of the wave is given by
where in this case we have
v = 334 m/s
f = 1481.2 Hz is the apparent in the source frame
So the wavelength is
Refer to the diagram shown below.
After 5 minutes (300 seconds):
The man travels north by (2 ft/s)*(300 s) = 600 ft
The woman, located at q, 500 east of p, begins walking south at 4 ft/s.
The distance separating them is
d₁ = √(600² + 500²) = 781.025 ft
After 20 minutes:
The man has traveled for 20 minutes (1200 s).
The woman has traveled for 15 minutes (900 s).
The man has moved (2 ft/s)*(1200 s) = 2400 ft north of p.
The woman has moved (4 ft/s)*(900 s) = 3600 ft south of q.
The distance separating them is
d₂ = √(6000² + 500²) = 6020.8 ft
The separation from d₁ to d₂ occurs in 15 minutes (900s).
Therefore the rate of separation is
Rate = (d₂ - d₁ ft)/(900 s) = (6020.8 - 781.025)/900 = 5.822 ft/s
or
Rate = (5.822 ft/s)*(60 s/min) = 349.32 ft/min
Answer: 349.32 ft/min (or 5.82 ft/s)
After 5 minutes (300 seconds):
The man travels north by (2 ft/s)*(300 s) = 600 ft
The woman, located at q, 500 east of p, begins walking south at 4 ft/s.
The distance separating them is
d₁ = √(600² + 500²) = 781.025 ft
After 20 minutes:
The man has traveled for 20 minutes (1200 s).
The woman has traveled for 15 minutes (900 s).
The man has moved (2 ft/s)*(1200 s) = 2400 ft north of p.
The woman has moved (4 ft/s)*(900 s) = 3600 ft south of q.
The distance separating them is
d₂ = √(6000² + 500²) = 6020.8 ft
The separation from d₁ to d₂ occurs in 15 minutes (900s).
Therefore the rate of separation is
Rate = (d₂ - d₁ ft)/(900 s) = (6020.8 - 781.025)/900 = 5.822 ft/s
or
Rate = (5.822 ft/s)*(60 s/min) = 349.32 ft/min
Answer: 349.32 ft/min (or 5.82 ft/s)